Case 1: two people wake up in spaceships accelerating at 1g. They can measure or observe anything inside the room but not outside. They couldn't determine if they were on a spaceship or on earth. If they ever communicated in the future they would be the same age. Is this correct?

Case 2: one person wakes up in a room on earth, another on a spaceship accelerating 1g. Same measuring restrictions. Again neither could determine if they were on a spaceship or earth. However now if they communicated in the future they would find they are different ages. Is this correct?

I've heard acceleration from a rocket or gravity are the same (e.g. time slows down near a black hole). But case 2 above seems there is a difference?

1 Answer
1

The scenarios you've proposed and the conclusions you are asking about are correct. Your only misstep is in the final paragraph, where you imply that the difference between those two scenarios is contradictory. The difference between the scenarios is relative velocity, just as it would be with the standard "Twin Paradox", in which one twin stays on earth while the other undergoes a near-lightspeed journey.

The problem in the twin paradox is the symmetry-breaking induced by the necessity of accelerating the twin who leaves earth in order to compare ages (while the twin on earth undergoes no change in acceleration). Until you reverse directions and bring that twin back to earth, the observations/communications of the twins will be symmetric, i.e., they will each see the other as getting older faster. If you bring them together to compare, you have a non-symmetric situation, and the difference between the two twins becomes non-contradictory. You can read up on this easily enough, so I won't go into greater detail here.

In your first scenario, you can maintain symmetry between the rockets, so when you bring the two people together, they're the same age. In the second scenario, just as with the twin paradox, you won't find a contradiction until you try and bring the rocket traveler back to compare.

It occurs to me that it's worth pointing out explicitly that communication without changing the physical situation, i.e., the rocket keeps accelerating at 1g, won't reveal different ages between the participants.